Distributions are considered any population that has a scattering of data. It’s important to determine the kind of distribution that population has so we can apply the correct statistical methods when analyzing it.

## Types of Data in a Distribution

Typically discreet or continuous

### Discrete Distributions

Discrete= counted

### Continuous Distributions

Continuous = can take many different values

- Normal Distribution
- Lognormal
- Extreme value
- F distribution
- Chi Square
- Exponential distribution
- Has a constant failure rate as it will always have the same shape parameters.

- T Student distribution
- Weibull Distribution

#### Non-normal distributions

Also see Non-normal distributions

## Evaluating a Distribution

- Look for hard stops
- # of values
- Evaluate the shape
**Exponential**– hockey stick- Has a constant failure rate as it will always have the same shape parameters.

- Gamma
- Contains variable shape and scale parameters.

**Uniform**– Flat bar, constant: used to test random # generators- everything has the same probability.**Log-normal**(lognormal)– Used in maintainability analysis – bringing broken tools back on line tends to follow lognormal.- takes on different shapes depending on the mean and standard deviation.
- http://www.free-six-sigma.com/lognormal-distribution.html (Lognormal distribution)

**Bi-modal**– 2 sources of data coming into a single process screen.- Weibull
- Assumes many shapes depending upon the shape, scale, and location parameters.Effect of Shape parameter B on Weibull distribution:
- If the shape parameter B is 1, it becomes identical to exponential distribution.
- If 2, then Rayleigh distribution.
- If between 3 and 4, then Normal distribution.

- Assumes many shapes depending upon the shape, scale, and location parameters.Effect of Shape parameter B on Weibull distribution:

## Symmetric Distribution

Both sides of the mean match & mirror each other.

## Asymmetric Distribution

Both sides of the mean do NOT match.

## Skewed Distribution

The data set has outliers. Skewness is a measure of the lack of symmetry.

When the outliers are high on one side, the mean will be > Median

## Comments (2)

Hi Ted –

It appears that the above Binomial link isn’t working.

https://sixsigmastudyguide.com/sampling-with-replacement/

Thank you sir!

Jeff

Thanks, Jeff. It should be all set now!